Production of Optimized DEM Using IDW Interpolation Method (Case Study; Jam and Riz Basin-Assaloyeh)

INTRODUCTION

Topographic conditions of the watershed are one of the integrated physical factors which can be seen in nature. In other word, every part of the land characterized with an elevation which in most cases is more similar to the other points of the catchments, however using some indicated points as ground control points the other unknown point will identified. Estimation and assessment method of continuous variable value in area where there is no any experimental model and the ground control points are scattered, interpolation method can be used (Bob and Booth, 2000). In fact, interpolation method indicates the continuous spatial variations as identified surface. For the mentioned purpose IDW can be used in interpolation method. In this way, the value of each variable will be calculated base on neighbors mean in specific distance. So that, distance inverse is weighted from unknown points. The distance of unknown point's decreases from control points is related to their neighboring so the value weight of the nearest points will increase and unknown points will be estimated by use of surrounding points of a certain radius (Childs and Colin, 2004). When the power is zero, the distance's role can be ignored and unknown points reached from the neighbor points mean. While the power increases the distance affect would increase and closer distances reached to the higher weight. Usually, in IDW model is recommended to use a power higher than 1 (Meyers, 1994). The gained results layers of this method depend on searching radius and number of neighbor points which including the recent points. It can be decided to have an equal weight for the all directions and specified circle or ellipse which included unknown points in their center, if there is no any trend of direction for the remind data. The value of point which placed in ellipse which is not clear so it can be calculate using the existent points in ellipse. Then the space of every point will be measured. Finally the distance inverse will be computed according to the unknown pint so, the power obtains and its average will be considered for unknown points (Tali, 2004). In fact the power degree is a weight which is given to the related distances. Therefore, the point's distances increases from unknown point with lower weight in assessment of these points (Johnston and Kevin, 2001). A DEM is a numerical representation of topography, usually made up of equal-sized cells, each with a value of elevation. Its simple data structure and widespread availability have made it a popular tool for land characterization. Because topography is a key parameter controlling the function of natural ecosystems, DEM_s are highly useful to deal with ever-increasing environmental issues. Since many GIS applications rely on DEM_s, their intrinsic quality is critical, particularly for hydrologic modeling (Beven and Krikby, 1979; O’loughlin, 1986; Darboux et al., 2002) or soil distribution analysis (Bloschl and Sivalapan, 1995; Chaplot et al., 2000; Mc Bratney et al., 2003). The applications of DEM_s are very diverse, ranging from basin characterization which requires the investigation of large areas, to the evaluation of water pounding capacity at the clod level that requires very accurate height estimates. The development of numerical representations of landscapes over large area with a high resolution DEM is thus one of the most important scientific challenges of environmental studies. Several factors affect the quality of DEM_S. An initial source of errors can be attributed to the data collection. The quality of the estimation of height for each data points depends on the technology applied. Some of the methods available include the ground based or airborne automatic laser scanner which is of a very high resolution and suitable for relatively small areas (Darboux and Huang, 2003). Conventional topographic surveys with a laser theodolite use at the meso scale and with a centimetric accuracy and use of existing contour maps, stereoscopic air-photos or high resolution satellite imagery for the characterization of large areas (Toutin and Cheng, 2002; Poon et al., 2005). The use of DEM_S generated from low density altitude data points may result in over estimations of secondary topographic attributes such as the upslope contributing areas (Quinn et al., 1991; Zhang and Montgomery, 1994; Brasington and Richards, 1998) and under estimation of slope gradient (Chaplot et al., 2000; Thompson et al., 2001; Toutin, 2002). Other sources of errors include the spatial structure of altitude and the interpolation technique for DEM generation (Wood and Fisher, 1993; Wilson and Gallant, 2000). The topographic modeler must be particularly careful when selecting the techniques for interpolation between the initial sampling data points of altitude, as this could have a great effect on the quality of DEM_S. Many interpolation techniques exist. The question of which is the most appropriate in different contexts is the central question and has stimulated several comparative studies of interpolation accuracy (Weber and Englund, 1992, 1994; Carrara et al., 1997; Robeson, 1997). The existing literature, however, tends to be equivocal as to which interpolation techniques is the most accurate. Some studies (Creutin and Obled, 1982; Laslett and Mc Brantney, 1990; Laslett, 1994; Burrough and Mc Donnell, 1998; Zimmerman et al., 1999; Wilson and Gallant, 2000) indicate that among the many existing interpolation techniques, geostatistical ones better than the others.

In particular, Zimmerman et al. (1999) showed that Kriging yielded better estimations of altitude than IDW did, irrespective of the land form type and sampling pattern. This result is probably due to the ability of Kriging to take into account the spatial structure of data. However, in other studies (Weber and Englund, 1992; Gallichand and Marcotte, 1993; Brus et al., 1996; Declercq, 1996; Aguilar et al., 2005), neighborhood approaches such as IDW or radial basis functions were an accurate as Kriging or even better. Keranc-henko and Bullock (1999) have compared IDW, ordinary Kriging and log normal ordinary Kriging for the soil properties (phosphorous (p) and potassium (k) of 30 experimental fields. They have found that if the underlying data set is log normally distributed and contains less than 200 points, log normal ordinary Kriging generally outperforms both ordinary Kriging and IDW; otherwise ordinary Kriging is more successful. Chaplot et al. (2006) in their study accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density concluded that under conditions of high C.V, strong spatial structure and strong anisotropy, IDW performs slightly better than the other method. Robinson and Metternich (2006) in their study testing the performance of spatial interpolation techniques for mapping soil properties have used IDW method and concluded that IDW is able to interpolate subsoil PH with a sensible accuracy. Ruhaak (2006) has developed a program which easily interpolates the type of 3D scattered data and produces satisfied results. For the interpolation algorithm has used a modified version of IDW. In this research, preparing the optimized digital elevation model of Jam and Riz basin was studied by use of Inverse Distance Weighting and utilization of GIS technique. With identified cell size of pixels in network with 3 m and determining the rotation angle and measure of axis of standard deviation ellipse, optimized radius was calculated in standard ellipse by use of statistical method. Then optimized power was automatically derived in ArcGIS 9.2 environment. In this method the number of neighbor's points was selected with four repetition points of 3, 5, 7 and 15. However 8 digital elevation models were gained after the mentioned processes. Finally, digital elevation models of 1 to 8 were compared with control points using compare means test in SPSS11.5 software which shown the IDW-3 whit the best conditions recommended as the optimized model.